1. Functions review;
2. Determining Domain and Range;
3. Reading graphs;
4. Evaluating the difference quotient
5. Families of functions from 9 parent functions
6. Piece-wise functions
6. End behavior of functions
7. Even and Odd functions
8. Operations on functions
9. Composition of functions
10. Sections 3.1-3.6
1. What is a function? function notation?
2. How do you determine the domain of a function from its equation? graph?
3. How do you read a graph from the function notation? (f(x)>0)
4. What are the 9 parent functions? their properties? How do you transform them in the plane?
5. How do you determine whether a function is even or odd from the graph? From the equation?
6. How do you determine the end behavior of a function from its equation or graph?
7. How do you do add, subtract, multiply and divide functions? and how is the new function related to the first 2?
8. What is composition of functions?
1. Determine if a relation is a function from its equation or its graph. Read/write function notation.
2. Determine the domain of a function from its graph or equation.
3. Read graph to determine characteristics of a function (f(x)>0)
4. Evaluate the difference quotient for polynomial functions.
5. Be able to graph the 9 parent functions, their transformations and determine domain and range for each using interval notation.
6. Graph and write equations of a piece-wise function made up of transformed parent functions
7. Determine the end behavior of a function and write it in limit notation.
8. Complete graph of an even/odd function
9. Determine algebraically whether a function is even, odd or neither.
10. Add, subtract, mult. and divide functions.
11. Be able to do composition of functions and decompose functions.
Quiz #1:
reading graphs, domain/range, functions, difference quotient
Quiz #2:
Parent functions and their transformations
Quiz #3
Piece-wise functions, Even and Odd functions, Operations on functions and composition of function
Mid-Sept. - First of Oct.
1. Rates of Change (difference quotient);
2. Inverse functions (See 3.7)
1. How are slope and the difference quotient related and how do they relate to rates of change?
2. What is a one-to-one function? What are inverse functions? How are inverse functions related graphically and analytically?
1. Ability to find rate of change with many different functions.
2. Determine if functions are one-to-one. Restrict the domain of a function to make it one-to-one. Prove analytically that 2 functions are inverses. Graph the inverse of a function.
Quiz on Rates of change and inverse functions.
October (middle 2 weeks)
1. PSAT Practice & Review
2. Quadratics
1. What types of questions? What format? What are some strategies for taking the Math SAT?
2. What are quadratic functions? their graphs? their properties? their equations?
1. Be familiar with the different test formats, strategies.
2. Be able to recognize a quadratic equation in any form, change from one form to another, draw a graph giving roots, vertex and another point.
1. Practice questions provided by College Board.
2. Quiz on Quadratics
End of Oct - Beg. of November (2 1/2 weeks - 3 weeks)
Polynomial Functions
1. What is a polynomial function? What are roots? factors? remainders? and what is their signifance to the graph of the polynomial function?
2. How do I find the roots without a calculator?
1.a. Identify polynomial functions.
b. Identify roots from the graph and write equation from the graph and roots.
c. Be able to perform long division and synthetic division to test roots (solutions).
d. Identify divisor and remainder as a point on the curve.
e. Graph a polynomial function given an equation
in factored form.
2. a. Know and use the Rational Roots theorem to determine possible solutions, then continue as before, using synthetic division to test solutions.
b. Find all solutions, real or non-real.
1. How do you add, subtract, mult., divide and simplify rational expressions and complex rational fractions?
2. How do you solve rational equations? What is an extraneous solution?
3. What is a rational function? What does its graph look like? How do you determine the roots, asymptotes, domain and range of rational functions?
1. Simplify, add, subtract, mult. & divide rational expressions, including complex fractions.
2. Solve rational equations, determine extraneous solutions and check solutions.
3. a. Finding the limits of rational functions graphically and analytically.
b. Graph 1/x and the transformations of 1/x and give the domain and range.
c. Graph rational functions of the form (ax+b)/(cx+d) and identify the transformations of the parent function (1/x) and give the domain and range.
d. Graph rational functions with more than one vertical asymptote and give the domain and range.
e. Graph rational functions with deg. of numerator > deg. of denominator where:
i. factors cancel and leave holes,
ii. factors do not cancel and the graph has oblilque asymptotes.
Quiz #1: Simplifying rational expressions and solving rational equations
Quiz #2: Graphing rational functions (transformations of 1/x)
Quiz #3: Graphing rational functions with more than one vertical asymptote and rational functions with holes
Quiz #4: Graphing rational functions with oblique asymptotes
January - first 2 weeks of Feb.
1. Polynomial, Rational and Absolute value inequalities
2. Exponents
3. Exponential Equations - solving graphically
4. Graphs of exponential functions
5. Modeling with Exponential functions
1. How are Polynomial, Rational and Absolute value inequalities different from equations and how do you solve them?
2. What are the rules of exponents?
3. How do you solve an exponential equation graphically?
4. What does an exponential function look like? How do you determine domain and range and how do you graph it without a calculator?
5. What are some real world applications of exponential functions?
1. Solve Polynomial, Rational and Absolute value inequalities analytically and graphically.
2. Apply rules of exponents to simplify expressions or equations.
3. Simplify equations and solve them graphically with caluculator.
4. a. Give the domain, range, intercepts, asymptote and end behavior (using limit notation) of an exponential function and tell if is increasing or decreasing.
b. Graph an exponential function with and without a calculator show all important features in part a.
5. Use exponential functions and equations to solve real world problems, including compounding interest & population growth
Quiz #1 Simplifying exponential expressions and solving exponential equations.
Quiz #2 Graphing exponential functions
Test on all of Exponential functions and applications
Last 2 weeks of February
Logarithms
1. What is a logarithm?
2. What are the properties of logs?
3. What does a logarithmic function look like?
4. How to logs help us solve exponential equations that we used to have to solve only with calculator?
March
1. Right Triangle Trigonometry
2. Law of Sines & Law of Cosines
3. Right Triangle Trigonometry and the Unit Circle
Chapter 8
1. What are the 6 basic trig ratios?
2. What do you use to solve non-right triangles?
3. What is the unit circle and how are the special right triangles and trig ratios related to the it?
1. Define and use 6 trig ratios to solve right triangles and real world problems involving right triangles.
2. Use law of sines and law of cosines to solve non-right triangle problems.
3. Apply the special right triangles to the unit cirle and define the trig ratios for sine, cosine and tangent from 0 to 2 pi.
Quiz #1 right triangle trig, law of sines and law of cosines.
Quiz #2 Special values and the unit circle
April
1. Graphs of the Trig functions
2. Modeling with the trig functions
2. Determining Domain and Range;
3. Reading graphs;
4. Evaluating the difference quotient
5. Families of functions from 9 parent functions
6. Piece-wise functions
6. End behavior of functions
7. Even and Odd functions
8. Operations on functions
9. Composition of functions
10. Sections 3.1-3.6
2. How do you determine the domain of a function from its equation? graph?
3. How do you read a graph from the function notation? (f(x)>0)
4. What are the 9 parent functions? their properties? How do you transform them in the plane?
5. How do you determine whether a function is even or odd from the graph? From the equation?
6. How do you determine the end behavior of a function from its equation or graph?
7. How do you do add, subtract, multiply and divide functions? and how is the new function related to the first 2?
8. What is composition of functions?
2. Determine the domain of a function from its graph or equation.
3. Read graph to determine characteristics of a function (f(x)>0)
4. Evaluate the difference quotient for polynomial functions.
5. Be able to graph the 9 parent functions, their transformations and determine domain and range for each using interval notation.
6. Graph and write equations of a piece-wise function made up of transformed parent functions
7. Determine the end behavior of a function and write it in limit notation.
8. Complete graph of an even/odd function
9. Determine algebraically whether a function is even, odd or neither.
10. Add, subtract, mult. and divide functions.
11. Be able to do composition of functions and decompose functions.
reading graphs, domain/range, functions, difference quotient
Quiz #2:
Parent functions and their transformations
Quiz #3
Piece-wise functions, Even and Odd functions, Operations on functions and composition of function
2. Inverse functions (See 3.7)
2. What is a one-to-one function? What are inverse functions? How are inverse functions related graphically and analytically?
2. Determine if functions are one-to-one. Restrict the domain of a function to make it one-to-one. Prove analytically that 2 functions are inverses. Graph the inverse of a function.
2. Quadratics
2. What are quadratic functions? their graphs? their properties? their equations?
2. Be able to recognize a quadratic equation in any form, change from one form to another, draw a graph giving roots, vertex and another point.
2. Quiz on Quadratics
2. How do I find the roots without a calculator?
b. Identify roots from the graph and write equation from the graph and roots.
c. Be able to perform long division and synthetic division to test roots (solutions).
d. Identify divisor and remainder as a point on the curve.
e. Graph a polynomial function given an equation
in factored form.
2. a. Know and use the Rational Roots theorem to determine possible solutions, then continue as before, using synthetic division to test solutions.
b. Find all solutions, real or non-real.
2. Rational Equations
3. Rational Functions
2. How do you solve rational equations? What is an extraneous solution?
3. What is a rational function? What does its graph look like? How do you determine the roots, asymptotes, domain and range of rational functions?
2. Solve rational equations, determine extraneous solutions and check solutions.
3. a. Finding the limits of rational functions graphically and analytically.
b. Graph 1/x and the transformations of 1/x and give the domain and range.
c. Graph rational functions of the form (ax+b)/(cx+d) and identify the transformations of the parent function (1/x) and give the domain and range.
d. Graph rational functions with more than one vertical asymptote and give the domain and range.
e. Graph rational functions with deg. of numerator > deg. of denominator where:
i. factors cancel and leave holes,
ii. factors do not cancel and the graph has oblilque asymptotes.
Quiz #2: Graphing rational functions (transformations of 1/x)
Quiz #3: Graphing rational functions with more than one vertical asymptote and rational functions with holes
Quiz #4: Graphing rational functions with oblique asymptotes
2. Exponents
3. Exponential Equations - solving graphically
4. Graphs of exponential functions
5. Modeling with Exponential functions
2. What are the rules of exponents?
3. How do you solve an exponential equation graphically?
4. What does an exponential function look like? How do you determine domain and range and how do you graph it without a calculator?
5. What are some real world applications of exponential functions?
2. Apply rules of exponents to simplify expressions or equations.
3. Simplify equations and solve them graphically with caluculator.
4. a. Give the domain, range, intercepts, asymptote and end behavior (using limit notation) of an exponential function and tell if is increasing or decreasing.
b. Graph an exponential function with and without a calculator show all important features in part a.
5. Use exponential functions and equations to solve real world problems, including compounding interest & population growth
Quiz #2 Graphing exponential functions
Test on all of Exponential functions and applications
2. What are the properties of logs?
3. What does a logarithmic function look like?
4. How to logs help us solve exponential equations that we used to have to solve only with calculator?
2. Law of Sines & Law of Cosines
3. Right Triangle Trigonometry and the Unit Circle
Chapter 8
2. What do you use to solve non-right triangles?
3. What is the unit circle and how are the special right triangles and trig ratios related to the it?
2. Use law of sines and law of cosines to solve non-right triangle problems.
3. Apply the special right triangles to the unit cirle and define the trig ratios for sine, cosine and tangent from 0 to 2 pi.
Quiz #2 Special values and the unit circle
2. Modeling with the trig functions
matching applet